Measurement of diffusion coefficients in multicomponent gas mixtures by the reversed-flow technique

Summary The reversed-flow method for measurement of gas diffusion coefficients in binary mixtures is now extended to simultaneous determination of effective diffusion coefficients for each substance in a multicomponent gas mixture. The method is applied to six ternary mixtures, each consisting of two gaseous hydrocarbons and H₂, He or N₂. The results are in agreement with a limiting case of the Stefan-Maxwell equations.     

Diffusion coefficients from stopped-flow gas chromatography

Summary Mutual diffusion coefficients of two gases A and B can be determined in an empty gas chromatographic column by letting component B enter at an intermediate position of the column and continuously flow through a part only of it, as a carrier gas. The other component A is injected in a small amount instantaneously at the closed end of the column with the detector placed at the other end. By repeatedly stopping and then restoring after a short time the flow of B, narrow extra peaks are produced on the chromatographic elution curve, owing to diffusion of A into B. An equation is derived giving the area under the curve of each stop-peak as a function of time of the corresponding stop. Plotting the experimental data according to this equation permits the determination of the diffusion coefficient of A into B. Some results obtained by this method show negligible variations with changes in the experimental parameters.     

Distinct Diffusion in Macromolecule‐Solvent Mixtures

Summary: The specificity of interactions between pairs of molecules cannot be explicitly given by experimental transport coefficients such as intra‐ or mutual diffusion coefficients. But a microscopic interpretation of the transport properties exists, where distinct diffusion coefficients (DDCs) are related to preferential, correlated motion among distinct molecules. Since in general the DDCs do not play the role of an indicator for molecular self‐association phenomena if not compared with some appropriate standard, here we propose DDCs of hard spheres at the second order of volume fraction as new standard coefficients. The analysis based on these novel DDCs is designed to study intermolecular interaction between macromolecule and solvent. Comparisons of the novel non‐ideal with previous ideal reference states were done, and their combined use is shown to reinforce information conveyed by the usual velocity correlation analysis. The comparison of novel hard sphere standards with real DDCs, corresponding to an homologous chemical series of poly(ethylene glycol)‐water mixtures, provides a look at this polymer‐solvent mixture in a dilute and semi‐dilute regime.

Comparison between real (calculated by using Equation (5)–(7) and experimental data) and hard‐sphere based distinct diffusion coefficients for PEG 200 (1: Dequation/tex2gif-stack-1.gif; 2: Dequation/tex2gif-stack-2.gif and 3: Dequation/tex2gif-stack-3.gif).     

Mutual diffusion coefficients of heptane isomers in nitrogen: a molecular dynamics study

The accurate knowledge of transport properties of pure and mixture fluids is essential for the design of various chemical and mechanical systems that include fluxes of mass, momentum, and energy. In this study we determine the mutual diffusion coefficients of mixtures composed of heptane isomers and nitrogen using molecular dynamics (MD) simulations with fully atomistic intermolecular potential parameters, in conjunction with the Green-Kubo formula. The computed results were compared with the values obtained using the Chapman-Enskog (C-E) equation with Lennard-Jones (LJ) potential parameters derived from the correlations of state values: MD simulations predict a maximum difference of 6% among isomers while the C-E equation presents that of 3% in the mutual diffusion coefficients in the temperature range 500-1000 K. The comparison of two approaches implies that the corresponding state principle can be applied to the models, which are only weakly affected by the anisotropy of the interaction potentials and the large uncertainty will be included in its application for complex polyatomic molecules. The MD simulations successfully address the pure effects of molecular structure among isomers on mutual diffusion coefficients by revealing that the differences of the total mutual diffusion coefficients for the six mixtures are caused mainly by heptane isomers. The cross interaction potential parameters, collision diameter σ(12), and potential energy well depth ?(12) of heptane isomers and nitrogen mixtures were also computed from the mutual diffusion coefficients.     

A new gas chromatographic methodology for the estimation of the composition of binary gas mixtures

The relatively new technique of reversed-flow gas chromatography (RFGC) is used to determine the diffusion coefficients of pure gases into gas mixtures (D(mix)(exp)). The pure gases are CO and CO(2), and the mixtures consist of H(2) and He in various volume percentage compositions. A linear regression analysis of D(mix)(exp) of CO and CO(2) in various mixtures of H(2) and He against the percentage composition (X(H2) or X(He)) of the mixtures at different temperatures results in an empirical equation relating D(mix)(exp) to the corresponding theoretical values of the diffusion coefficients of CO and CO(2) in the pure gases H(2) and He, as they are calculated from the Fuller-Schettler-Giddings equation. The empirical equation shows that the diffusion coefficient of an analyte gas in a gas mixture is the partial sum of its diffusion coefficients in the component gases, therefore making possible the determination of the mole fractions of the components of the mixture. The found percentage volume compositions are very close to those determined independently by routine gas chromatography, indicating that the proposed RFGC methodology could be successfully applied to the accurate determination of the volume composition of binary gas mixtures.     

Activity coefficients in aqueous mixtures of hydrochloric acid and lanthanum chloride at 25°C

Activity coefficients of hydrochloric acid in aqueous solutions of lanthanum chloride were determined by an emf method at 25°C over an ionic strength range 0.05–3 mol-kg^–1. Harned's rule was obeyed within experimental error by the acid in all the mixtures. However, the fit with Pitzer's equations was not as good as the Harned rule fit, even though the effects of higher-order electrostatic terms were considered. Activity coefficients for the salt in the mixtures were derived using the Pitzer equations and fitted to the Harned equation, whereupon Harned's rule was found to be valid for the salt up to an ionic strength of 0.3 mol-kg^–1 only.     

On the interpretation of ternary diffusion measurements in low-molecular weight fluids by dynamic light scattering

Dynamic light scattering (DLS) allows for efficient measurement of physical transport properties in fluids. It is now a well established technique for determination of mutual mass diffusion coefficients in binary mixtures and multicomponent macromolecular solutions. More recently, ternary systems of low-molecular weight compounds have been analyzed by DLS where it was found that only one of the two mass diffusion modes can be observed. In this work, a theoretical interpretation of these findings is provided. For this purpose, a simple theory is developed that describes the observed signals. Thereby, it can be shown that both diffusion modes contribute to the signal but one mode is strongly enhanced for situations typically encountered in DLS experiments. The developed theory thus clarifies the relationship between ternary DLS measurements and other diffusion experiments. It provides the practical basis for quantitative analysis of DLS experiments in ternary low-molecular weight fluids.     

Correlation of the mutual diffusion coefficients of binary liquid mixtures

A correlative UNIDIF model for the mutual diffusion coefficients of binary liquid mixtures is developed using statistical thermodynamics and the absolute reaction rate theory. In this model, a mole fraction average of the logarithm of the pure-component limiting diffusion coefficients is taken as a reference term. The model expresses the excess part of the diffusion coefficient relative to this reference term in a form similar to that of a UNIQUAC equation which comprises two parts due to the combinatorial and residual contributions. The combinatorial part depends on the molecular sizes and shapes. The residual part includes two binary interaction parameters, which are obtained from data regression, for each binary mixture. Mutual diffusion coefficients of nonpolar+nonpolar, nonpolar+polar and polar+polar fluid mixtures are correlated in this study. Optimal binary interaction parameters are presented. Correlation results using the UNIDIF model for mutual diffusion coefficient are satisfactory and are superior to those from other methods.     

Measurements of molecular and thermal diffusion coefficients in ternary mixtures

Thermal diffusion coefficients in three ternary mixtures are measured in a thermogravitational column. One of the mixtures consists of one normal alkane and two aromatics (dodecane-isobutylbenzene-tetrahydronaphthalene), and the other two consist of two normal alkanes and one aromatic (octane-decane-1-methylnaphthalene). This is the first report of measured thermal diffusion coefficients (for all species) of a ternary nonelectrolyte mixture in literature. The results in ternary mixtures of octane-decane-1-methylnaphthalene show a sign change of the thermal diffusion coefficient for decane as the composition changes, despite the fact that the two normal alkanes are similar. In addition to thermal diffusion coefficients, molecular diffusion coefficients are also measured for three binaries and one of the ternary mixtures. The open-end capillary-tube method was used in the measurement of molecular diffusion coefficients. The molecular and thermal diffusion coefficients allow the estimation of thermal diffusion factors in binary and ternary mixtures. However, in the ternaries one also has to calculate phenomenological coefficients from the molecular diffusion coefficients. A comparison of the binary and ternary thermal diffusion factors for the mixtures comprised of octane-decane-1-methylnaphthalene reveals a remarkable difference in the thermal diffusion behavior in binary and ternary mixtures.     

Activity coefficients in mixed-electrolyte solutions at 25°C: Na-formate + NaCl system

Activity coefficients for NaCl in aqueous mixtures with Na-Formate were determined at 25°C from emf measurements for different total ionic strengths. At each total ionic strength studied, the measurements were carried out at different ratios of the Na-Formate to NaCl ionic strengths. The experimental activity coefficients were fitted using the Harned equation and the treatments of Scatchard et al. and Pitzer et al. Finally, the excess Gibbs energy of these mixtures was also calculated.     

Diffusion Measurements To Understand Dynamics and Structuring in Solutions Involving a Homologous Series of Ionic Liquids

The self-diffusion coefficients of each of the components in mixtures containing pyridine and each of the homologous series 1-alkyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imides in acetonitrile were determined using NMR diffusometry (i. e., Pulsed Gradient Spin Echo). The nature of solvation was found to change significantly with the proportion of salt in the mixtures. Increased diffusion coefficients (when corrected for viscosity) for the molecular components were observed with increasing proportion of ionic liquid and with increasing alkyl chain length on the cation. Comparison of the molecular solvents suggests increased interactions in solution of the pyridine with other components of the mixture, consistent with the proposed interactions shown previously to drive changes in reaction kinetics. Discontinuities were seen in the diffusion data for each species in solution across different ionic liquids between the hexyl and octyl derivatives, suggesting a change in the structuring in solution as the alkyl chain on the cation changes and demonstrating the importance of such when considering homologous series.     

锂离子在石墨负极材料中扩散系数的测定

锂离子电池是以各种碳材料为负极而起来的一 种新型电池,成功地解决了以 为负极瓣锂可充电电池的安全性问题,已经应用于锂离子电池的负极材料有石墨和石油焦炭,正在研究的负极材料有热解碳,石墨化碳纤维,硼炭或硼炭氮化合物以及锡基氧化物等[1],石墨的比容量要比石油焦炭的比容量高一倍左右,其理论比容量372mA.h.g^-1,但锂离子在石墨材料中的扩散系数比较低,限制了以其为负极材料的电池的大电流充放电能力,锂离子在电极材料中的扩散系数可以用多种电化学方法测量得到,主要有：电位间歇滴定方法（PITT）（Potentiostatic Intermittent Titratiobn Technique)^[2,3,4,6],恒电流间歇滴定法（GITT）（Galvanostatic Intermittent Titration Technology)^[6],电流脉冲松弛法（CPR）（Current Pulse Relaxation Method)^[3,6]和交流阻抗法（A－C Technology)^[4,5,6],GITT,CPR,A-C等方法测定锂离子扩散系数时,由于相变发生处dE/dy值不容易准确得到（相变时,dE/dy→0）,此时测得的扩散系数误差比较大,PITT方法测定锂离子扩展系统,不存在这个问题,能比较准确地测定整个嵌入组成范围内的锂离子扩散系数。     

Diffusion with molecular association in chloroform + triethylamine and chloroform + dioxane mixtures

The Taylor dispersion method is used to measure the binary mutual diffusion coefficients of chloroform + triethylamine and chloroform +1,4-dioxane at 25°C. The components of these mixtures associate, forming chloroform-triethylamine and chloroform-dioxane, (chloroform)₂-dioxane molecular complexes. A modified Hartley-Crank equation is developed to express the binary diffusion coefficient as a weighted average of the diffusion coefficients of the free molecules and the molecular complexes. Counterintuitively, the contribution made by each molecular complex to the overall diffusion coefficient vanishes when the concentration of the complex reaches its maximum value. The measured and fitted diffusion coefficients agree within 3% or better over the complete composition range.     

Flow injection analysis methods for determination of diffusion coefficients

Two flow injection analyses (FIA) methods for the determination of diffusion coefficients in a straight single tube FIA system were developed. Based on the analytical solution of the convection-diffusion equation, linear relationships of the logarithmic values of the dispersion coefficient (D) and the half-peak width (W_1/2) with the diffusion coefficient (D_m) were obtained. Experiments were designed to verify these methods. For example, for potassium hexacyanoferrate (III) a D_m value of 0.72 × 10⁵ cm² s⁻¹ was found versus a literature value of 0.76 × 10⁵ cm² s⁻¹ (error, 5%). For potassium hexacyanoferrate (II) a D_m value of 0.67 × 10⁵ cm² s⁻¹ was obtained versus a literature value of 0.63 × 10⁵ cm² s⁻¹ (error, 6%). The diffusion coefficients of some important biomedical compounds, such as dopamine, epinephrine, norepinephrine and ascorbic acid, were then determined. The values of 10⁵ D_m/cm² s⁻¹ are 0.60 ± 0.03, 0.44 ± 0.02, 0.60 ± 0.01 and 0.68 ± 0.06, respectively.     

Calculation of Combined Diffusion Coefficients from the Simplified Theory of Transport Properties

The aim of this study is to check if it is possible to use the combined diffusion coefficients introduced by Murphy at equilibrium in a two-temperature model (electron temperature T_e different from that of heavy species T_h), such as that defined by Devoto and Bonnefoi for transport properties. On the one hand, the two-temperature (2-T) theory of transport properties was established by Devoto and Bonnefoi by separating electrons and heavy species because of their mass difference. Their simplified theories allow the calculation of transport coefficients (except diffusion) out of thermal equilibrium, but it has to be noted that when T_e tends toward T_h, the results are those obtained with an equilibrium calculation. On the other hand, Murphy's combined diffusion coefficients describe the diffusive mixing of two nonreactive ionized gases at equilibrium. First, the exact combined diffusion coefficients of Murphy are calculated for an Ar–N₂ (50 wt.%) mixture at atmospheric pressure. Expressions of combined diffusion coefficients are then obtained by using the simplified theory of Bonnefoi at thermal equilibrium. The results of the calculation of combined diffusion coefficients from the simplified theory of transport properties, assuming Te=Th, are compared with those of Murphy at equilibrium. It is shown that large discrepancies occur as soon as the ionization degree is over 10%. These results prove that the simplified 2-T theory of transport coefficients cannot be used for the treatment of diffusion, probably because the mass flux of electrons is no longer constrained. Thus, a new theory of transport coefficients has to be developed, taking into account the coupling of electrons and heavy species.     

Hydrodynamic approximation for distinct diffusion coefficients

The distinct diffusion coefficient is a measure of the coupling of the diffusive motions of two particles. It is given as the integral over a velocity cross correlation rather than the velocity self correlation that determines the self-diffusion coefficient. A hydrodynamic approximation for the distinct diffusion coefficient is proposed and then tested by comparison with data for a wide range of non-ionic binary mixtures. The hydrodynamic approximation gives negative distinct diffusion coefficients and is in qualitative agreement with most of the data. In many cases, deviations from the model results can be explained in terms of interactions which are not accurately treated by the model.     

On measurement of thermal diffusion coefficients in multicomponent mixtures

We investigate the steady-state separation of the individual components of an incompressible multicomponent liquid mixture in a narrow two-dimensional thermogravitational column. Analytic working equations for measuring thermal diffusion coefficients analogous to the existing equations for a binary mixture are derived. Similar to the binary results, we find that when compositional variation has negligible effect on fluid density and vertical diffusive flux can be ignored, molecular diffusion does not affect steady-state separation. However, when compositional effects on density are taken into account, molecular diffusion does affect the bulk convective flow and the steady-state separation of the components. There may be also two distinct trends in the velocity and separation profiles. With one or more negative thermal diffusion coefficients, there may be more than one convection cell resulting in oscillatory behavior of separation. The working equations presented can be used to measure thermal diffusion coefficients of multicomponent mixtures. Such measurements have not yet been reported in the literature.     

Effect of macromolecular polydispersity on diffusion coefficients measured by Rayleigh interferometry

Rayleigh interferometry has been extensively used for the precise determination of diffusion coefficients for binary and ternary liquid mixtures. For ternary mixtures, the 2x2 matrix of multicomponent diffusion coefficients is obtained. Polydispersity adds complexity to the meaning of these measured diffusion coefficients. Here we discuss three important issues of polydispersity regarding the diffusion measurements extracted from this interferometric technique. First, we report novel equations for the extraction of diffusion moments from the Rayleigh interferometric pattern. These moments are used to define polydispersity parameters for macromolecular systems. We have experimentally determined mean diffusion coefficients and polydispersity parameters for aqueous solutions of poly(ethylene glycol) and poly(vinyl alcohol) at 25 degrees C. Aqueous solutions of poly(ethylene glycol) mixtures were used to examine the accuracy of the polydispersity parameters. Second, we compare Rayleigh interferometry to dynamic light scattering. Specifically, we have performed diffusion measurements on the same system using both techniques. To our knowledge, no direct experimental comparison between dynamic light scattering and classical methods for the measurements of diffusion coefficients has been previously reported in relation to polydispersity. We find that substantial discrepancies (i.e., 1 order of magnitude) between the mean diffusion coefficients obtained from these two different techniques can be observed when polydispersity is large. Third, for two-solute mixtures with one polydisperse solute, we report a novel corrective procedure for extracting accurate ternary diffusion coefficients from Rayleigh interferometry. Computer simulations were used to examine the accuracy of the extracted ternary diffusion coefficients.     

FTIR imaging coupled with multivariate analysis for study of initial diffusion of different solvents in cellulose acetate butyrate films

Fourier transform infrared (FTIR) spectroscopic imaging was used to study the initial diffusion of different solvents in cellulose acetate butyrate (CAB) films containing different amounts of acetyl and butyryl substituents. Different solvents and solvent/non-solvent mixtures were also studied. The FTIR imaging system allowed acquisition of sequential images of the CAB films as solvent penetration proceeded without disturbing the system. The interface between the non-swollen polymer and the initial swelling front could be identified using multivariate data analysis tools. For a series of ketone solvents the initial diffusion coefficients and diffusion rates could be quantified and were found to be related to the polar and hydrogen interaction parameters in the Hansen solubility parameters of the solvents. For the solvent/non-solvent system the initial diffusion rate decreased less than linearly with the weight-percent of non-solvent present in the solution, which probably was due to the swelling characteristic of the non-solvent. For a given solvent, increasing the butyryl content of the CAB increased the initial diffusion rate. Increasing the butyryl content from 17 wt.% butyryl to 37 wt.% butyryl produced a considerably larger increase in initial diffusion rate compared to an increase in butyryl content from 37 wt.% to 50 wt.% butyryl.     

Diffusion and partition coefficients of small organic solvents in molten miscible polymer blends: Correlations with thermodynamic interactions

The transport properties of small organic molecules in molten poly(vinyl chloride) (PVC)/atactic poly(methyl methacrylate) (PMMA) blends and their homopolymers were studied with inverse gas chromatography. The elution profiles resulting from various organic solvents and different experimental conditions were used for measuring diffusion and partition coefficients. With the van Deemter equation and retention volumes at infinite dilution, diffusion coefficients of 10^?7 to 10^?8 cm²/s and partition coefficients of 10–50 were calculated. The dependence of the diffusion and partition coefficients on experimental variables such as the blend concentration, temperature, and solute nature was examined. The presence of PMMA in PVC blends affected the sorption behavior of the PVC matrix up to a certain concentration. Beyond that, it was hard to derive any composition–diffusivity dependence. On the contrary, the diffusion and partition coefficients were greatly influenced by changes in the temperature and by the nature of the solute. For those solutes (e.g., chlorinated hydrocarbons) showing stronger interactions with polymer blends (higher negative values for the Flory–Huggins interaction parameter χ₁₍₂₃₎), higher diffusion and partition coefficients were obtained. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 267–279, 2004